%   ORIGINAL: h4/finite__map/FRANGE__FUPDATE__DOMSUB
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/finite__map/FRANGE__FUPDATE: !y x f. h4/finite__map/FRANGE (h4/finite__map/FUPDATE f (h4/pair/_2C x y)) = h4/pred__set/INSERT y (h4/finite__map/FRANGE (h4/finite__map/DRESTRICT f (h4/pred__set/COMPL (h4/pred__set/INSERT x h4/pred__set/EMPTY))))
% Assm: h4/finite__map/fmap__domsub: !k fm. h4/finite__map/fdomsub fm k = h4/finite__map/DRESTRICT fm (h4/pred__set/COMPL (h4/pred__set/INSERT k h4/pred__set/EMPTY))
% Goal: !v k fm. h4/finite__map/FRANGE (h4/finite__map/FUPDATE fm (h4/pair/_2C k v)) = h4/pred__set/INSERT v (h4/finite__map/FRANGE (h4/finite__map/fdomsub fm k))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_finiteu_u_maps_FRANGEu_u_FUPDATE]: !y x f. h4/finite__map/FRANGE (h4/finite__map/FUPDATE f (h4/pair/_2C x y)) = h4/pred__set/INSERT y (h4/finite__map/FRANGE (h4/finite__map/DRESTRICT f (h4/pred__set/COMPL (h4/pred__set/INSERT x h4/pred__set/EMPTY))))
% Assm [h4s_finiteu_u_maps_fmapu_u_domsub]: !k fm. h4/finite__map/fdomsub fm k = h4/finite__map/DRESTRICT fm (h4/pred__set/COMPL (h4/pred__set/INSERT k h4/pred__set/EMPTY))
% Goal: !v k fm. h4/finite__map/FRANGE (h4/finite__map/FUPDATE fm (h4/pair/_2C k v)) = h4/pred__set/INSERT v (h4/finite__map/FRANGE (h4/finite__map/fdomsub fm k))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q75297,TV_Q75293]: ![V_f, V_g]: (![V_x]: s(TV_Q75293,happ(s(t_fun(TV_Q75297,TV_Q75293),V_f),s(TV_Q75297,V_x))) = s(TV_Q75293,happ(s(t_fun(TV_Q75297,TV_Q75293),V_g),s(TV_Q75297,V_x))) => s(t_fun(TV_Q75297,TV_Q75293),V_f) = s(t_fun(TV_Q75297,TV_Q75293),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_finiteu_u_maps_FRANGEu_u_FUPDATE, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x, V_f]: s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_frange(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fupdate(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_insert(s(TV_u_27b,V_y),s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_frange(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_compl(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))))))))).
fof(ah4s_finiteu_u_maps_fmapu_u_domsub, axiom, ![TV_u_27b,TV_u_27a]: ![V_k, V_fm]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fdomsub(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm),s(TV_u_27a,V_k))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_compl(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_k),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))))).
fof(ch4s_finiteu_u_maps_FRANGEu_u_FUPDATEu_u_DOMSUB, conjecture, ![TV_u_27b,TV_u_27a]: ![V_v, V_k, V_fm]: s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_frange(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fupdate(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_k),s(TV_u_27b,V_v))))))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_insert(s(TV_u_27b,V_v),s(t_fun(TV_u_27b,t_bool),h4s_finiteu_u_maps_frange(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_fdomsub(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_fm),s(TV_u_27a,V_k)))))))).
